Mathematics

Question

Steve made a sign for his room that is shaped like a triangle. It is 4.5 feet long and 3 feet high. He wants to make another sign that is shaped like a triangle and similar to the first sign. The new sign will be 4 feet high.

Part A

Write a proportion that Steve can use to find the length, x, of the new sign.

Part B

What is the length, in feet, of the new sign? Make sure to show your work and explain your reasoning.

1 Answer

  • Answer: PART A : [tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]

    PART B : 5.9 FEET

    Step-by-step explanation:

    Length of the first sign = 4.4 feet

    height of the first sign = 3 feet

    Length of the second sign = x feet

    height of the second sign = 4 feet

    If two shapes are similar , then the ratio of their sides are equal,

    That is ;

    [tex]\frac{h_{1}}{h_{2} }[/tex] = [tex]\frac{L_{1}}{L_{2} }[/tex]

    PART A

    [tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]

    PART B

    [tex]\frac{4.4}{x}[/tex] = [tex]\frac{3}{4}[/tex]

    cross multiplying , we have

    3x = 4.4 x 4

    3x = 17.6

    Divide through by 3

    x = 17.6/3

    x = 5.86666666666667

    x≈ 5.9 feet

    Therefore , the length of the new sign is 5.9 feet

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